The von Neumann-Wold model for isometries on Hilbert space has been important in many parts of mathematics from prediction theory for stationary stochastic processes to the function theory of Hardy spaces. Part of its power lies in its relative simplicity. Various researchers have considered the structure of commuting n-tuples of isometries including Berger-Coburn-Lebow in the mid seventies. In this talk, I'll discuss some recent joint work with Bercovici and Foias in which one attempts to obtain more detailed descriptions of n-tuples in special cases. The results relate to canonical models and invariant subspaces.